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Migration Velocity Analysis. 01. Outline. Motivation. Estimate a more accurate velocity model for migration. Theory. Tomographic migration velocity analysis. Numerical Results. Conclusions. 02. Motivation. Forward modeling. d = L m. Kirchhoff Migration. m mig = L T d. - PowerPoint PPT Presentation
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Migration Velocity AnalysisMigration Velocity Analysis
01
OutlineOutline
MotivationMotivationEstimate a more accurate velocity model for migrationEstimate a more accurate velocity model for migration
Tomographic migration velocity analysis Tomographic migration velocity analysis
02
TheoryTheory
Numerical ResultsNumerical Results
ConclusionsConclusions
Motivation
03
d = L m
mmig = LT d
Forward modeling
Kirchhoff Migration
Function of velocity: LT (s)
Inaccurate velocity model
mmig = LT d
Motivation
04
True velocity model
True velocity model
Kirchhoff Migration Image
Inaccurate velocity model
Inaccurate velocity model
Kirchhoff Migration Image
Goal of MVA:To get a more accurate velocity model
Structure error
Position error
OutlineOutline
MotivationMotivationEstimate a more accurate velocity model for migrationEstimate a more accurate velocity model for migration
Tomographic Migration Velocity AnalysisTomographic Migration Velocity Analysis
05
TheoryTheory
Numerical ResultsNumerical Results
ConclusionsConclusions
Theory
06
The fundamental principle underlying MVA is that the migration image of the same reflector should be the same for different source, when using the correct velocity, so pre-stack common image gather (CIG) provides the information of whether the migration velocity is correct and how far away it is from the true velocity.
Theory
07
Common Image Gather ( CIG)
different CSGs
CSG #1
CSG #2
CSG #3
Point scatterer
Theory
08
Common Image Gather ( CIG)
Prestack migration
s
KM of CSG #1
x
z
x0
x
z
KM of CSG #2
x0
x
z
KM of CSG #3
x0
CIG
Theory
09
Tomographic MVAxx0
z
xx0
z
s
z
CIG
Flat
xx0
z
Correct Velocity
x
z
2000 m/s
x0
Theory
10
Tomographic MVA
Curved
Incorrect Velocity
1500 m/s
x
z
x0
xx0
z
s
z
CIG
xx0
z z
xx0
Theory
11
Offset (km) 1
CIG
-1
CIG
Offset (km) 1-1
Tomographic MVA
Hyperbolic approximation
Zh2 = Z0
2 + A h2
picking depth,
Zh
Zh
Z0
zero-offset depth,Z0
Depth residual reference depth
Usually choose Z0 as Zref
ΔZ = Zh - Zref Zref
x0
h
offset, h
Theory
12
Tomographic MVA
Convert depth residual to time residual
x0xs xgFind the source-receiver pair by ray tracing to obey Snell’s lawθ1 θ2
x0xs xg
R reflector with reference depth Zref
R’ reflector with picked depth Zh t’ = LSR’ s + LRG st = LSR s + LRG s
Δt = t’ - t
Theory
13
For a small slowness perturbation
traveltime, raypath operator, background slowness.
t = L st L s
Δs
Δt = t’-t0 = LΔs = L(s’-s0)Parameterize the model as a grid of cells
traveltime residual for the raypath , slowness purturbation in grid cell
Δti = Σ Δsj Δlij
n
j=1Δti i Δsj
j
Update the slowness with a steepest descent method
Back project along the raypaths to get
Δti Δsj
sj(k+1) = sj
(k+1) – α Δsj(k+1)
Tomographic MVAUpdate the slowness
Theory
14
Misfit function
Iteration will stop when all curved events in CIG are flatten.
picked depth residual for offset in CIG of the iteration
Tomographic MVA
Fmisfit = Σ Σ (Δzij )2 i=1 j=1
m n(k) (k)
Δzij j i k(k)
15
Migration velocity model s0
TheoryTheory
Predict travel time by eikonal solver
Pre-stack KM , form CIGs
Pick the reference depth residual (usually zero-offset)
Find ray paths connecting the reflector to both S and R positions
Convert depth residual to travel time residual
Update velocity model by back projecting the traveltime residuals along the raypaths.
Work Flow:
Migration velocity model sk
Pick the depth residual automatically
Observed data
All events are flattened?
Y
MVA finished !
N
OutlineOutline
MotivationMotivationEstimate a more accurate velocity model for migrationEstimate a more accurate velocity model for migration
Tomographic migration velocity analysis Tomographic migration velocity analysis
16
TheoryTheory
Numerical ResultsNumerical Results
ConclusionsConclusions
Numerical Results
17
2D Synthetic Model
KM image CIGTrue velocity model
H. Sun. 1999
Numerical Results
18
2D Synthetic Model
H. Sun. 1999
Homogeneous velocity model KM image CIG
Numerical Results
19
2D Synthetic Model
H. Sun. 1999
Final updated velocity model KM image CIG
Initial Migration VelocityInitial Migration Velocity
0000
1818
1.51.5
Horizontal Distance (km)Horizontal Distance (km)
Dep
th (
km)
Dep
th (
km) 2.12.1
1.51.5
(km
/s)
(km
/s)
KM Image with Initial VelocityKM Image with Initial Velocity0000
18 km18 km
1.51.5
Dep
th (
km)
Dep
th (
km)
00
1.51.5
Dep
th (
km)
Dep
th (
km)
KMVA Velocity Changes in the 1st IterationKMVA Velocity Changes in the 1st Iteration
5050
00
(m
/s)
(m /s
)
KM Image with Initial VelocityKM Image with Initial Velocity
KM Image with Updated VelocityKM Image with Updated Velocity
9 km9 km
12601260
De
pth
(m
)D
ep
th (
m)
2 km2 km
10701070
12601260
De
pth
(m
)D
ep
th (
m)
10701070
KMVA CIGs with Initial VelocityKMVA CIGs with Initial Velocity
00
1.51.5
Dep
th (
km)
Dep
th (
km)
KMVA CIGs with Updated VelocityKMVA CIGs with Updated Velocity
0000
18 km18 km
1.51.5
Dep
th (
km)
Dep
th (
km)
00
1.51.5
Dep
th (
km)
Dep
th (
km)
KMVA Velocity Changes in the 1st Iteration (CPU=6)KMVA Velocity Changes in the 1st Iteration (CPU=6)
5050
00
(m
/s)
(m /s
)
WMVA Velocity Changes in the 1st Iteration (CPU=1)WMVA Velocity Changes in the 1st Iteration (CPU=1)
5050
00
(m
/s)
(m /s
)
WM Image with Initial VelocityWM Image with Initial Velocity
WM Image with Updated VelocityWM Image with Updated Velocity
9 km9 km
12601260
De
pth
(m
)D
ep
th (
m)
2 km2 km
10701070
12601260
De
pth
(m
)D
ep
th (
m)
10701070
WMVA CIGs with Initial VelocityWMVA CIGs with Initial Velocity
00
1.51.5
Dep
th (
km)
Dep
th (
km)
WMVA CIGs with Updated VelocityWMVA CIGs with Updated Velocity
KM Image with Initial VelocityKM Image with Initial Velocity 9 km9 km
12601260
De
pth
(m
)D
ep
th (
m)
2 km2 km
10701070
KM Image with KMVA Updated VelocityKM Image with KMVA Updated Velocity
12601260
De
pth
(m
)D
ep
th (
m)
10701070
KM Image with WMVA Updated VelocityKM Image with WMVA Updated Velocity
12601260
De
pth
(m
)D
ep
th (
m)
10701070
OutlineOutline
MotivationMotivationEstimate a more accurate velocity model for migrationEstimate a more accurate velocity model for migration
Tomographic migration velocity analysis Tomographic migration velocity analysis
26
TheoryTheory
Numerical ResultsNumerical Results
ConclusionsConclusions
27
• Pre-stack migration with inaccurate velocity can bring curved events in CIGs, which provides the opportunity for migration velocity analysis.
• Iterative tomographic MVA can estimate better migration velocity and improve the migration image.
ConclusionsConclusions
• Question: what are the advantages and disadvantages of migration velocity analysis compared to velocity estimation in data domain ?
Numerical Results
20
2D Field Data
H. Sun. 1999
00
00
18181.51.5
Initial migration velocity from NMOInitial migration velocity from NMO
Dep
th (
km
)D
epth
(k
m)
2.12.1
1.51.5
(k
m /s
)(k
m /s
)
Horizontal distance (km)Horizontal distance (km)
Numerical Results
21
2D Field Data
H. Sun. 1999
00
00
18181.51.5
KM image with the initial velocityKM image with the initial velocity
Dep
th (
km
)D
epth
(k
m)
Horizontal distance (km)Horizontal distance (km)
Numerical Results
22
2D Field Data
H. Sun. 1999
00
1.51.5
KM CIGs with the initial velocityKM CIGs with the initial velocityD
epth
(k
m)
Dep
th (
km
)
1.21.2
Numerical Results
23
KM Image with Initial VelocityKM Image with Initial Velocity
00
00
1.51.5
Dep
th (
km)
Dep
th (
km)
00
1.51.5
Dep
th (
km)
Dep
th (
km)
KM Image with Updated VelocityKM Image with Updated Velocity 1818
Numerical Results
24
KM Image with Initial VelocityKM Image with Initial Velocity
KM Image with Updated VelocityKM Image with Updated Velocity
9 km9 km
12601260
Dep
th (
m)
Dep
th (
m)
2 km2 km
10701070
12601260
Dep
th (
m)
Dep
th (
m)
10701070
Numerical Results
25
KMVA CIGs with Initial VelocityKMVA CIGs with Initial Velocity
00
1.51.5
Dep
th (
km
)D
epth
(k
m)
KMVA CIGs with Updated VelocityKMVA CIGs with Updated Velocity